I will use this blog post as my "attack plan" of learning mathematics from the beginning, starting with proofs and discrete mathematics and ending with dynamical models in biology. This post is subject to change at any time.
Goal: Re-teach myself mathematics in areas appropriate for bioinformatics.
Timeline
Dynamical models in biology requires prerequisites of Math 250 (Linear Algebra) and Calc IV (Elementary Differential Equations). Thus, the following classes are part of the expected coursework for this entire project, should I learn every prerequisite needed for each class:
- Precalculus*
- Linear Algebra*
- Calculus I*
- Calculus II*
- Multivariable Calculus*
- Elementary Differential Equations*
- Real analysis (optional)
- Dynamical Models in Biology*
In addition, I am adding the following subjects to better round out my knowledge in mathematics:
- Introduction to Mathematical Reasoning (proofs)
- Logic (optional)
- Discrete and Probabilistic Models in Biology
Each class/subject takes one semester's worth of time, a total of 5 years worth of learning at most. As it stands, most ultralearning projects choose to shorten that timeline. Young's ultralearning project itself, the MIT Challenge, condensed 4 years worth of MIT's computer science courses into one year.
I find myself reaching for a less ambitious roadmap. After all, I will still be working, and moreover, *I have taken almost all of these courses before. As such, the learning curve is flattened a bit, with less time needed on introductory courses and more time spent on relearning important concepts and maintaining accuracy. For example, I don't expect myself to spend a lot of time on precalculus as a subject, since I am already adept at it.
Consequently, I will not be digesting 5 years' worth of information. I approximate this ultralearning timeline to take one year, learning 2.5 years' worth of information within that time span. I am giving myself permission to extend or decrease up to half a year.
Parts of Young's project intersect with mine, with Calculus, Linear Algebra, and Logic being part of the MIT OCW. I will use his resources where available but otherwise supplement these courses with textbooks that I obtain myself.
Textbooks/Resources
- Khan Academy
- Linear Algebra (Friedberg, Insel, and Spence)
- Calculus (Stewart)
- Dynamical Models in Biology (Farkas)
- https://www.math.rutgers.edu/academics/undergraduate/201-course-materials/270-338/1255-course-notes
- An Introduction to Mathematical Reasoning (Eccles)
- Book of Proof (Hammack)
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